nLab timelike curve

Definition

For $(X,g)$ a Lorentzian spacetime, a tangent vector $v \in T_x X$ is called

• timelike if $g(v,v) \lt 0$;

• lightlike if $g(v,v) = 0$;

• spacelike if $g(v,v) \gt 0$.

A curve $\gamma : \mathbb{R} \to X$ is called timelike or lightlike or spacelike if all of its tangent vectors $\dot \gamma$ are, respectively.

Related concepts

• event

• time

• light cone, future cone

• static spacetime, stationary spacetime

• Penrose limit, pp-wave spacetime

• Lorentzian spacetime, Lorentzian geometry

• causal order, causal locality